# Small prismated tesseractic tetracomb

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Small prismated tesseractic tetracomb | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Euclidean |

Notation | |

Bowers style acronym | Spittit |

Coxeter diagram | x4o3o3x4o () |

Elements | |

Tera | 6N tesseracts, 4N cuboctahedral prisms, N rectified tesseracts, N small disprismatotesseractihexadecachora |

Cells | 16N tetrahedra, 32N triangular prisms, 4N+24N+24N cubes, 8N cuboctahedra |

Faces | 64N triangles, 24N+24N+96N squares |

Edges | 48N+96N |

Vertices | 32N |

Vertex figure | Triangular antifastegium, edge lengths 1 (base edges of triangular prism) and √2 (all other edges) |

Related polytopes | |

Army | Spittit |

Regiment | Spittit |

Conjugate | Quasiprismated tesseractic tetracomb |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | R_{5} |

Convex | Yes |

Nature | Tame |

The **small prismated tesseractic tetracomb** or **spittit**, also called the **runcinated tesseractic tetracomb** is a convex uniform tetracomb. 1 rectified tesseract, 2 small disprismatotesseractihexadecachora, 3 tesseracts, and 3 cuboctahedral prisms join at each vertex of this tessellation. As the name suggests, it is the runcination of the tesseractic tetracomb.

## Vertex coordinates[edit | edit source]

The vertices of a small prismated tesseractic tetracomb of edge length 1 are given by all permutations of:

- ,

where i , j , k , and l range over the integers.

## Representations[edit | edit source]

A small prismated tesseractic tetracomb has the following Coxeter diagrams:

- x4o3o3x4o () (full symmetry)
- x3o3o4x *b3x () (half symmetry)

## External links[edit | edit source]

- Klitzing, Richard. "spittit".
- Wikipedia contributors. "Runcinated tesseractic honeycomb".